Place raspberries and water in a medium saucepan over medium-high heat. Using a potato masher or a fork, crush the berries. Bring the berries to a simmer, then lower temperature to medium-low and simmer for about 2 minutes.

Remove pan from heat and pour berries into a fine-mesh strainer set over a glass measuring cup. Using the back of a ladle or spoon, press on the berries to squeeze out as much juice as possible. Discard seeds.

Return raspberry juices to the pan, then add the sugar and lemon juice. Bring to a boil and simmer for about 4-5 minutes until mixture reduces slightly. Remove from heat and chill in refrigerator to cool completely.

In a stand mixer fitted with the whisk attachment, whip the heavy cream until stiff peaks form. Transfer whipped cream to a separate bowl, return bowl to the mixer, and replace whisk attachment with paddle attachment.

To the mixer, add the mascarpone cheese, sugar, ¾ cup of the raspberry syrup, and vanilla. Beat on high until combined. Add about a cup of the whipped cream and continue beating until incorporated. Gently fold in the rest of the whipped cream.

One at a time, dip the ladyfingers in the raspberry syrup until soaked but not soggy; arrange in an even layer along the bottom of an 8-inch square dish. Spread half of the the mascarpone filling on top of the ladyfingers.

Using a zester, microplane, or cheese grater, grate half of the white chocolate evenly on top. Place another layer of raspberry syrup-soaked ladyfingers on top of the filling.

Spread half of the remaining filling on top of the ladyfingers. Transfer remaining filling to a pastry bag fitted with a large round tip, and pipe the filling evenly over the tiramisu. Grate the rest of the white chocolate on top.

Cover with plastic wrap and refrigerate for at least 6 hours, preferably overnight.